www.gusucode.com > econ 案例源码程序 matlab代码 > econ/VerifyExplicitlyCreatedDiffuseStateSpaceModelExample.m

    %% Verify Explicitly Created Diffuse State-Space Model
% An important step in state-space model analysis is to ensure that the
% software interpretes the state and observation equation matrices as you
% intend. Use |disp| to help you verify the diffuse state-space model.
%%
% Define a diffuse state-space model, where the state equation is an AR(2)
% model, and the observation equation is the difference between the current
% and previous state plus the observation error.  Symbolically, the
% state-space model is
%
% $$\left[ {\begin{array}{*{20}{c}}{{x_{1,t}}}\\{{x_{2,t}}}\\{{x_{3,t}}}\end{array}}
% \right] = \left[
% {\begin{array}{*{20}{c}}0.6&0.2&0.5\\1&0&0\\0&0&1\end{array}} \right]\left[
% {\begin{array}{*{20}{c}}{{x_{1,t - 1}}}\\{{x_{2,t - 1}}}\\{{x_{3,t -
% 1}}}\end{array}} \right] + \left[ {\begin{array}{*{20}{c}}{0.3} \\
% 0 \\ 0\end{array}} \right]u_{1,t}$$
%
% $${y_t} = \left[ {\begin{array}{*{20}{c}}1&-1&0\end{array}}
% \right]\left[
% {\begin{array}{*{20}{c}}{{x_{1,t}}}\\{{x_{2,t}}}\\{{x_{3,t}}}\end{array}}
% \right]+0.1\varepsilon_t.$$
%
% Assume the initial state distribution is diffuse.
%%
% There are three states: $x_{1,t}$ is the AR(2) process,
% $x_{2,t}$ represents $x_{1,t-1}$, and $x_{3,t}$ is the AR(2) model
% constant.
%%
% Define the state-transition matrix.

% Copyright 2015 The MathWorks, Inc.

A = [0.6 0.2 0.5; 1 0 0; 0 0 1];
%%
% Define the state-disturbance-loading matrix.
B = [0.3; 0; 0];
%%
% Define the measurement-sensitivity matrix.
C = [1 -1 0];
%%
% Define the observation-innovation matrix.
D = 0.1;
%%
% Specify the state-space model using |dssm|.  Identify the type of initial
% state distributions (|StateType|) by noting the following: 
%
% * $x_{1,t}$ is an  AR(2) process with diffuse initial distribution.
% * $x_{2,t}$ is the same AR(2) process as $x_{1,t}$.
% * $x_{3,t}$ is the constant 1 for all periods.
%
StateType = [2 2 1];
Mdl = dssm(A,B,C,D,'StateType',StateType);
%%
% |Mdl| is a |dssm| model.
%%
% Verify the diffuse state-space model using |disp|.
disp(Mdl)
%%
% |Cov0| has infinite variance for the AR(2) states.